Given a \((c,d,n)\) -LDPC code, let \(m=nc/d\) . By counting constraints it is easy to see that the dimension of an LDPC code is at least \(n-m = n(1-\frac{c}{d})\) , so the rate is at least \(1-\frac{c}{d}\) .
Spielman described in his thesis [1]} the following expansion property,
